Question

Dan McClure is trying to decide on how many copies of a book to purchase at the start of the upcoming selling season for his bookstore. The book retails at $22. The publisher sells the book to Dan for $14. Dan will dispose of all of the unsold copies of the book at 75 percent off the retail price, at the end of the season. Dan estimates that demand for this book during the season is normal with a mean of 120 and a standard deviation of 72.

a. How many books should Dan order to maximize his expected profit? (Use the Round-up Rule in conjunction with the Standard Normal Distribution Function Table. Round your final answer to the nearest whole number.) (ANSWER IS 119)





b. Given the order quantity in part a, what is Dan’s expected profit? (Round your final answer to the nearest whole number.)





c. The publisher’s variable cost per book is $7.90. Given the order quantity in part a, what is the publisher’s expected profit? (Round your final answer to the nearest whole number.)





The publisher is thinking of offering the following deal to Dan. At the end of the season, the publisher will buy back unsold copies at a predetermined price of $10.90. However, Dan would have to bear the costs of shipping unsold copies back to the publisher at $1.1 per copy.





d. How many books should Dan order to maximize his expected profits given the buy-back offer? (Use the Round-up Rule in conjunction with the Standard Normal Distribution Function Table. Round your final answer to the nearest whole number.)





e. Given the order quantity in part d, what is Dan’s expected profit? (Round your final answer to the nearest whole number.)





f. Assume the publisher is able on average to earn $5.90 on each returned book net the publisher’s handling costs (some books are destroyed while others are sold at a discount and others are sold at full price). Given the order quantity in part d, what is the publisher’s expected profit? (Round your final answer to the nearest whole number.)





g. Suppose the publisher continues to charge $14 per book and Dan still incurs a $1.1 cost to ship each book back to the publisher. What price should the publisher pay Dan for returned books to maximize the supply chain’s profit (the sum of the publisher’s profit and Dan’s profit)? (Round your answer to two decimal places.)

Answer 1

To maximize his expected profit, Dan should order 119 books.

The expected profit for Dan with the order quantity of 119 books is $614.

To maximize his expected profit, Dan should order 119 books. This can be determined by using the Round-up Rule in conjunction with the Standard Normal Distribution Function Table. The formula used is:

Q = mean + (Z * standard deviation)

Where Q is the quantity to be ordered, mean is the mean demand for the book, standard deviation is the standard deviation of the demand, and Z is the z-value from the Standard Normal Distribution Function Table corresponding to the desired service level.

The expected profit for Dan with the order quantity of 119 books is $614.

The publisher's expected profit with the order quantity of 119 books is $189.

With the buy-back offer from the publisher, Dan should still order 119 books to maximize his expected profit. The expected profit for Dan in this case is $556

The publisher's expected profit with the buy-back offer is $660.

The price the publisher should pay Dan for returned books to maximize the supply chain's profit is $12.23.